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The solution of the equations, by either analytical or numerical means, describes how the biological system behaves either over time or at equilibrium. There are many different types of equations and the type of behavior that can occur is dependent on both the model and the equations used. The model often makes assumptions about the system.
In mathematics, a free boundary problem (FB problem) is a partial differential equation to be solved for both an unknown function and an unknown domain. The segment Γ {\displaystyle \Gamma } of the boundary of Ω {\displaystyle \Omega } which is not known at the outset of the problem is the free boundary .
1.4 Biology. 1.5 Economics. 2 Other equations. Toggle Other equations subsection. ... This is a list of equations, by Wikipedia page under appropriate bands of their ...
The theory, which can be called a reaction–diffusion theory of morphogenesis, has become a basic model in theoretical biology. [2] Such patterns have come to be known as Turing patterns. For example, it has been postulated that the protein VEGFC can form Turing patterns to govern the formation of lymphatic vessels in the zebrafish embryo. [3]
Mackey-Glass equations; McKendrick–von Foerster equation in age structure modeling; Nernst–Planck equation in ion flux across biological membranes; Price equation in evolutionary biology; Reaction-diffusion equation in theoretical biology. Fisher–KPP equation in nonlinear traveling waves; FitzHugh–Nagumo model in neural activation
This is an energy balance which defines the position of the moving interface. Note that this evolving boundary is an unknown (hyper-)surface; hence, Stefan problems are examples of free boundary problems. Analogous problems occur, for example, in the study of porous media flow, mathematical finance and crystal growth from monomer solutions. [1]
A differential equation which may be solved with Bessel functions [13] Jacobi equation: 1 = + + + + + + + + Special case of the Darboux equation, integrable in closed form [14] Loewner differential equation: 1
What is the origin of homochirality in living organisms? In biological organisms, amino acids appear almost exclusively in the left-handed form and sugars in the right-handed form. Homochirality is an obvious characteristic of life on Earth, yet extraterrestrial samples contain largely racemic compounds. [7]